There are three salts that contain complex ions of chromium and have the molecular formula \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Treating \(0.27 \mathrm{~g}\) of the first salt with a strong dehydrating agent resulted in a mass loss of \(0.036 \mathrm{~g}\). Treating \(270 \mathrm{mg}\) of the second salt with the same dehydrating agent resulted in a mass loss of \(18 \mathrm{mg}\). The third salt did not lose any mass when treated with the same dehydrating agent. Addition of excess aqueous silver nitrate to \(100.0-\mathrm{mL}\) portions of \(0.100 M\) solutions of each salt resulted in the formation of different masses of silver chloride; one solution yielded 1430 \(\mathrm{mg} \mathrm{AgCl} ;\) another, \(2870 \mathrm{mg} \mathrm{AgCl}\); the third, \(4300 \mathrm{mg} \mathrm{AgCl}\). Two of the salts are green and one is violet. Suggest probable structural formulas for these salts, defending your answer on the basis of the preceding observations. State which salt is most likely to be violet. Would a study of the magnetic properties of the salts be helpful in determining the structural formulas? Explain.

Step by step solution

01

Analyze the dehydrating agent results

The first salt loses \(0.036 \mathrm{~g}\) mass after being treated with a dehydrating agent, the second salt loses \(18 \mathrm{mg}\) mass, and the third salt does not lose mass. Since each water molecule has a molar mass of \(18 \mathrm{g/mol}\), we can calculate the number of water molecules removed from each salt. First salt: Loss in mass: \(0.036 \mathrm{~g}\) Number of molecules removed: \(\frac{0.036 \mathrm{~g}}{18 \mathrm{g/mol}} = 0.002 \mathrm{mol}\) Second salt: Loss in mass: \(18 \mathrm{mg}\) Number of molecules removed: \(\frac{18 \mathrm{mg}}{18 \mathrm{g/mol}} = 0.001 \mathrm{mol}\)

02

Analyze the results from the addition of aqueous silver nitrate

For the three solutions treated with excess silver nitrate, different masses of silver chloride are precipitated: 1. 1430 \(\mathrm{mg} \mathrm{AgCl}\) 2. 2870 \(\mathrm{mg} \mathrm{AgCl}\) 3. 4300 \(\mathrm{mg} \mathrm{AgCl}\) These values suggest the number of chloride ions in each complex ion. Number of chloride ions: 1. \(\frac{1430 \mathrm{mg} / (143.32 \mathrm{g/mol}(\mathrm{AgCl}))}{0.002 \mathrm{mol}} = 3\) 2. \(\frac{2870 \mathrm{mg} / (143.32 \mathrm{g/mol}(\mathrm{AgCl}))}{0.001 \mathrm{mol}} = 2\) 3. \(\frac{4300 \mathrm{mg} / (143.32 \mathrm{g/mol}(\mathrm{AgCl}))}{0.001 \mathrm{mol}} = 4\)

03

Propose structural formulas and colors

Based on the results from Steps 1 and 2, we can propose structural formulas for the three salts, taking into account that two of them are green and one is violet: 1. \(\mathrm{[Cr(H_{2}O)_{4}Cl_{2}]Cl \cdot 2H_{2}O}\) (green) 2. \(\mathrm{[Cr(H_{2}O)_{5}Cl]Cl_{2} \cdot H_{2}O}\) (green) 3. \(\mathrm{[Cr(H_{2}O)_{6}]Cl_{3}}\) (violet) The higher oxidation state of the Cr(III) ion in the third salt would result in the violet color, while the lower oxidation states in the first two salts would yield green colors.

04

Discuss the magnetic properties

A study of the magnetic properties of the salts could help in determining the structural formulas since different structural formulas may show different magnetic behaviors. For instance, chromium in different oxidation states would have different unpaired electrons, leading to different magnetic properties. So, studying the magnetic properties would provide additional insight into the structural formulas of these salts.

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